Volume 38
–
No.12, January 2012
19 Figure 5b illustrates how the chain code of hand shape is
generated from boundary hand image. The boundary hand image is scanned from top left until the first boundary pixel is
found. This pixel is noted as starting pixel. In general, the location of the pixel is around the tip of middle finger because
the finger is generally longer than other fingers. The next boundary pixel is traced by clockwise movement and assigned
a code to this pixel by following Figure 5a. Figure 5c shows its chain code feature.
a
Close Up
} } } } } } } } }
} }
}
0 00 0 00 7
7 7
6
b
0000007767666766666666666666666666676666667666666666766 6666666666666667666666666656666666666666667677001112122
2212212221212212121221212121121122112212121222212222122 2122212211010000070776676666566665666566655666566566665
6566566665666566566665666565665665656666656665666667770 0101110111111101011121101111011112111121121112100000776
6666665665566555655566565555655565555556555655565565656 5566665656666556666665666656666556666565666656655665665
5666565655656666444444444444444444444444444444444444444 4444444444444444444444444444433434333333333323334332323
3323332233233323333332232332333333334334334334434334334 3333232332332322211101001000000000007070777777770707077
7706707770700700070000001010101132222111121212212322222 2212222223223322233232322323223223222223323223223232223
2232223232223222322222222222121110007007777677676767676 6667766766776777676767676767677666667676667667667666767
7777700001122222123222222222322222222222222222222222221 22222212222222222222222222222222232212222222112101
c
Figure 5. Extraction of chain cod, a 8-connectivity chain code, b hand shape chain code extraction, c chain code
feature vector
In this research chain code as shown in Figure 5c is used as a hand shape feature without any modification or
normalization process. Two hand shape chain code of the same user have tends to
unequal vector length and therefore dynamic time warping distance is used in this research to compute the similarity
degree of each other.
2.4 Dynamic Time Warping Distance
Dynamic Time Warping DTW is a well known technique to measure the similarity between two given time-dependant
sequences. One advantages of DTW is able to match of two feature vectors with unequal length. The feature vectors are
warped to match each other and the DTW distance is measured based on optimal warping path of two feature
vectors. The DTW distance of two vectors U and V with length m and
n respectively, can be expressed as follows:
, ,
n m
V U
DTW
1
1
, 1
, 1
, 1
min ,
,
j i
j i
j i
v u
d n
m
j i
ba se
2
, ,
, ,
,
3 ...
3 ,
2 ,
1 ;
... 3
, 2
, 1
n j
m i
The distance is commonly computed by creating the m by n distance matrix. The matrix contains element
γ
i, j
that represent the cumulative distance of warping path from
element 1,1 to i, j where 1≤ i ≤ m, 1 ≤ j ≤ n, therefore the
matrix is called cumulative distance matrix. Lets see the example of two chain code vectors U = 0 7 4 0,
and V = 1 0 7 5 1. The DTW distance of these vectors is 3. Figure 6a to 6e shows cumulative distance computation is
based on the column 1 to column 5 of V respectively, while the warping path from U to V is shown by shaded area in
Figure 6 f. A threshold value T is used to decide whether two chain
codes come from the same person genuine or not impostor. If the DTW score less than or equal with T then the tested
chain code is noted as authorized, otherwise the chain code is noted as not authorized.
d =d
Cumulative =Cumulative
Remark 1-0
2
1 1 + 0
1
Minimum 1-7
2
36 36 + 1
37 1-4
2
9 9 + 37
46 1-0
2
1 1 + 46
47
a
Volume 38
–
No.12, January 2012
20
D =d
Cumulative =Cumulative
Remark 0-0
2
0 + 1
1
Minimum 0-7
2
49 49 + 1
50 0-4
2
16 16 + 37
53 0-0
2
0 + 46 46
b
D =d
Cumulative =Cumulative
Remark 7-0
2
49 49 + 1
50 7-7
2
0 + 1
1
minimum 7-4
2
9 9 + 1
10 7-0
2
49 49 + 10
59
c
D =d
Cumulative =Cumulative
Remark 5-0
2
25 25 + 50
75 5-7
2
4 4 + 1
5 5-4
2
1 1 + 1
2
minimum 5-0
2
25 25 + 2
27
d
D =d
Cumulative =Cumulative
Remark 1-0
2
1 1 + 75
76 1-7
2
36 36 + 5
41 1-4
2
9 9 + 2
11 1-0
2
1 1 + 2
3
minimum
e
1 7
5 1
1 1
50 75
76 7
37 50
1 5
41 4
46 53
10 2
11 47
46 59
27
3
f
Figure 6. DTW distance computation of vector U = 0 7 4 0 and V=1 0 7 5 1, a, b, c, d, e represents
computation is based on column 1 to 5 of V respectively, f shaded area represents the warping path from U to V.
3. EXPERIMENTS AND RESULTS
The hand shape chain code feature and DTW distance have been applied for hand geometry verification system. The total
number of hand images used to test the system performance is 900 images that are generated from 12 samples from each of
the 75 users randomly selected. To know the impact of increasing the database size to the system performance then
these experiments create three type of database size is 25, 50 and 75 users with various numbers of reference samples in
template databases and various numbers of query image samples in testing database.
The performance of the verification system is obtained by matching each of testing hand images with all of the reference
hand images in the database. A matching is noted as a correct matching if the two hand images are from the same hand and
as incorrect if otherwise. This paper used FMR false match rate, FNMR false non match rate, system accuracy, and
receiver operation curve
ROC as indicators of the performance system.
A threshold value is used to determine the FNMR and FMR. This experiment tries various threshold values and each
threshold value will be produces a pair of FNMR and FMR. A pair of FNMR and FMR is selected as system performance
when the total of FNMR + FMR is smallest then the others and its threshold will be chosen as a threshold value of
system.
FNMR, FMR and success rate are computed as: 100
x a ccess
genuine of
tota l r a te
genuine r eject
of tota l
F NMR
4
100
x a ccess
impostor of
tota l r a te
impostor a ccpet
of tota l
F MR
5
100
F MR F NMR
Ra te Success
6
Table 1, Table 2 and Table 3 shows system performance by using database size 25, 50, and 75 users respectively with
varying in number of reference samples 2 to 8 samples in database. When the experiment use 2 samples as reference
this mean 10 of 12 remain sample images are used as test image. The tables show increasing the number of training
sample in database also tends to increase the success rate of the system. The best success rate achieved is about 84 when
using eight training samples in database for whole database size see the last row of Table 1, 2 and 3. The system
performance in database with 25 users is FNMR= 7.63, FMR=7.71, and success rate = 84.67, database with 50 users
is FNRM=7.88, FMR=7.99, and success rate = 84.13, while database with 75 users is FNRM=7.98, FMR=7.92, and
success rate = 84.10. Figure 7 shows graphics of genuine and impostor score
distribution and receiver operating curve by using database with 75 users. Overlapping area in Figure 7a will be effect
the system performance. The larger overlapping area, the higher the error rate system decrease the system
performance and vice versa.
Table 1. Performance of system by using template database contains 25 users
Number of
template samples
Database 25 users Threshold
Value FNMR
FMR Success
rate 2
218 13.40
13.25 73.35
3 211
11.11 11.38
77.51 4
207 10.84
10.78 78.37
5 207
10.97 10.90
78.12 6
204 10.00
10.35 79.65
7 203
10.17 9.98
79.85 8
192 7.63
7.71 84.67
